I have seen three ts and two out of the three messed up regularly between forgetting appts and messing up times. Currrent t is never late nor missed an appt every week for a whole year, she has also said she checked out of hospital early so she wouldn't miss an appt. She is very particular with her punctuality and this works well for me.
I am sorry your t messed up, it hurts

I am appalled that they didn't offer you a free session because if you missed their time you would have to pay, I think since they go on about respecting the clients and it being a mutual relationship where we are equals(although it is clearly not) its the least the t could do.